ISO/FDIS 12167-1

Plain bearings — Hydrostatic plain journal bearings with drainage grooves under steady-state conditions — Part 1: Calculation of oil-lubricated plain journal bearings with drainage grooves

This document applies to hydrostatic plain journal bearings under steady-state conditions. In this document, only bearings with oil drainage grooves between the recesses are taken into account. As compared to bearings without oil drainage grooves, this type needs higher power with the same stiffness behaviour. NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked against acceptable conditions. The use of them is equally admissible.

Paliers lisses — Paliers lisses radiaux hydrostatiques avec rainures d'écoulement fonctionnant en régime stationnaire — Partie 1: Calcul pour la lubrification des paliers lisses radiaux avec rainures d'écoulement

General Information

• Status: Not Published
• ICS: 21.100.10 - Plain bearings
• Technical Committee: ISO/TC 123/SC 8 - Calculation methods for plain bearings and their applications
• Drafting Committee: ISO/TC 123/SC 8 - Calculation methods for plain bearings and their applications
• Current Stage: 5020 - FDIS ballot initiated: 2 months. Proof sent to secretariat
• Start Date: 28-Mar-2023
• Completion Date: 28-Mar-2023

Relations

• Revises: ISO 12167-1:2016 - Plain bearings — Hydrostatic plain journal bearings with drainage grooves under steady-state conditions — Part 1: Calculation of oil-lubricated plain journal bearings with drainage grooves
• Effective Date: 06-Jun-2022

Standards Content (Sample)

DRAFT INTERNATIONAL STANDARD
ISO/DIS 12167-1
ISO/TC 123/SC 8 Secretariat: JISC
Voting begins on: Voting terminates on:
2022-09-14 2022-12-07
Plain bearings — Hydrostatic plain journal bearings with
drainage grooves under steady-state conditions —
Part 1:
Calculation of oil-lubricated plain journal bearings with
drainage grooves

Paliers lisses — Paliers lisses radiaux hydrostatiques avec rainures d'écoulement fonctionnant en régime

stationnaire —

Partie 1: Calcul pour la lubrification des paliers lisses radiaux avec rainures d'écoulement

ICS: 21.100.10
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
This document is circulated as received from the committee secretariat.
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL,
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
STANDARDS MAY ON OCCASION HAVE TO
BE CONSIDERED IN THE LIGHT OF THEIR
POTENTIAL TO BECOME STANDARDS TO
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NATIONAL REGULATIONS.
ISO/DIS 12167-1:2022(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
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RIGHTS OF WHICH THEY ARE AWARE AND TO
PROVIDE SUPPORTING DOCUMENTATION. © ISO 2022
---------------------- Page: 1 ----------------------
ISO/DIS 12167-1:2022(E)
DRAFT INTERNATIONAL STANDARD
ISO/DIS 12167-1
ISO/TC 123/SC 8 Secretariat: JISC
Voting begins on: Voting terminates on:
Plain bearings — Hydrostatic plain journal bearings with
drainage grooves under steady-state conditions —
Part 1:
Calculation of oil-lubricated plain journal bearings with
drainage grooves

Paliers lisses — Paliers lisses radiaux hydrostatiques avec rainures d'écoulement fonctionnant en régime

stationnaire —

Partie 1: Calcul pour la lubrification des paliers lisses radiaux avec rainures d'écoulement

ICS: 21.100.10
COPYRIGHT PROTECTED DOCUMENT
THIS DOCUMENT IS A DRAFT CIRCULATED
FOR COMMENT AND APPROVAL. IT IS
© ISO 2022
THEREFORE SUBJECT TO CHANGE AND MAY
This document is circulated as received from the committee secretariat.

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may

NOT BE REFERRED TO AS AN INTERNATIONAL

be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on STANDARD UNTIL PUBLISHED AS SUCH.

the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below

IN ADDITION TO THEIR EVALUATION AS

or ISO’s member body in the country of the requester. BEING ACCEPTABLE FOR INDUSTRIAL,

TECHNOLOGICAL, COMMERCIAL AND
ISO copyright office
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CP 401 • Ch. de Blandonnet 8
STANDARDS MAY ON OCCASION HAVE TO
BE CONSIDERED IN THE LIGHT OF THEIR
CH-1214 Vernier, Geneva
POTENTIAL TO BECOME STANDARDS TO
Phone: [phone]
WHICH REFERENCE MAY BE MADE IN
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NATIONAL REGULATIONS.
Website: www.iso.org ISO/DIS 12167-1:2022(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
Published in Switzerland
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
© ISO 2022 – All rights reserved
PROVIDE SUPPORTING DOCUMENTATION. © ISO 2022
---------------------- Page: 2 ----------------------
ISO/DIS 12167-1:2022(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

Introduction .................................................................................................................................................................................................................................v

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ..................................................................................................................................................................................... 1

3 Terms and definitions .................................................................................................................................................................................... 1

4 Symbols, terms and units ...........................................................................................................................................................................1

5 Bases of calculation and boundary conditions .................................................................................................................... 4

6 Method of calculation .....................................................................................................................................................................................6

6.1 General ........................................................................................................................................................................................................... 6

6.2 Load-carrying capacity ................................................................................................................................................................... 6

6.3 Lubricant flow rate and pumping power ........................................................................................................................ 8

6.4 Frictional power .................................................................................................................................................................................... 9

6.5 Optimization .......................................................................................................................................................................................... 10

6.6 Temperatures and viscosities ................................................................................................................................................ 11

6.7 Minimum pressure in recesses .............................................................................................................................................12

Annex A (normative) Description of the approximation method for the calculation

of hydrostatic plain journal bearings .........................................................................................................................................13

Annex B (informative) Example of calculation according to the method given in Annex A ..................23

Bibliography .............................................................................................................................................................................................................................31

iii
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ISO/DIS 12167-1:2022(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received (see www.iso.org/patents).

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and

expressions related to conformity assessment, as well as information about ISO's adherence to the

World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/

iso/foreword.html.

The committee responsible for this document is ISO/TC 123, Plain bearings, Subcommittee SC 8,

Calculation methods for plain bearings and their applications.

This third edition cancels and replaces the second edition (ISO 12167-1:2016), which has been

technically revised.
The main changes are as follows:
— subclause titles have been added;
— symbols have been corrected and added in Table 1;
— calculation values in Annex B have been corrected;
— adjustments have been made to ISO/IEC Directives, Part 2:2021;
— typographical errors have been corrected.
A list of all parts in the ISO 12167 series can be found on the ISO website.

Any feedback or questions on this document should be directed to the user’s national standards body. A

complete listing of these bodies can be found at www.iso.org/members.html.
© ISO 2022 – All rights reserved
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ISO/DIS 12167-1:2022(E)
Introduction

Hydrostatic bearings use external lubrication to support pressure on the bearings; thus, are less prone

to wear and tear, run quietly, and have wide useable speed, as well as high stiffness and damping

capacity. These properties also demonstrate the special importance of plain journal bearings in

different fields of application such as in machine tools.

Basic calculations described in this document may be applied to bearings with different numbers of

recesses and different width/diameter ratios for identical recess geometry.

Oil is fed to each bearing recess by means of a common pump with constant pumping pressure (system

p = constant) and through preceding linear restrictors, e.g. capillaries.

The calculation procedures listed in this document enable the user to calculate and assess a given

bearing design, as well as to design a bearing as a function of some optional parameters. Furthermore,

this document contains the design of the required lubrication system including the calculation of the

restrictor data.
© ISO 2022 – All rights reserved
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DRAFT INTERNATIONAL STANDARD ISO/DIS 12167-1:2022(E)
Plain bearings — Hydrostatic plain journal bearings with
drainage grooves under steady-state conditions —
Part 1:
Calculation of oil-lubricated plain journal bearings with
drainage grooves
1 Scope

This document applies to hydrostatic plain journal bearings under steady-state conditions.

In this document, only bearings with oil drainage grooves between the recesses are taken into account.

As compared to bearings without oil drainage grooves, this type needs higher power with the same

stiffness behaviour.

NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked

against acceptable conditions. The use of them is equally admissible.
2 Normative references

The following documents, in whole or in part, are normatively referenced in this document and are

indispensable for its application. For dated references, only the edition cited applies. For undated

references, the latest edition of the referenced document (including any amendments) applies.

ISO 3448, Industrial liquid lubricants — ISO viscosity classification

ISO 12167-2:2021, Plain bearings — Hydrostatic plain journal bearings with drainage grooves under

steady-state conditions — Part 2: Characteristic values for the calculation of oil-lubricated plain journal

bearings with drainage grooves
3 Terms and definitions
No terms and definitions are listed in this document.

ISO and IEC maintain terminology databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Symbols, terms and units
Symbols and units are defined in Table 1.
Table 1 — Symbols, terms and units
Symbol Term Unit
a Inertia factor 1
A Land area m
lan
Relative land area 1
lan
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ISO/DIS 12167-1:2022(E)
Table 1 (continued)
Symbol Term Unit
A Recess area m
b Width perpendicular to the direction of flow m
π ×D
 
b Width of axial outlet b = −+lb m
ax ax cG
 
 
b Width of circumferential outlet ()bB=−l m
c cax
b Width of drainage groove m
B Bearing width m
c Stiffness coefficient N/m
c Specific heat capacity of the lubricant (p = constant) J/kg·K
C Radial clearance m
d Diameter of capillaries m
D Bearing diameter (D : shaft; D : bearing; D ≈ D ≈ D ) m
J B J B
e Eccentricity (shaft displacement) m
f Relative film thickness [ f = h/C ] 1
f Relative film thickness at ϕϕ= 1
en,i 1,i
Relative film thickness at ϕϕ= ′
f 1
2,i
ex,i
F Load-carrying capacity (load) N
F Radial force in recess i N
F Horizontal component of the resultant force of recesses N
F Vertical component of the resultant force of recesses N
F* Characteristic value of load-carrying capacity 1
Characteristic value of effective load-carrying capacity 1
eff
Characteristic value of effective load-carrying capacity for N = 0 1
eff,0
h Local lubricant film thickness (clearance gap height) m
h Oil film thickness at entrance edge of recess m
h Oil film thickness at exit edge of recess m
h Minimum lubricant film thickness (minimum clearance gap height) m
min
h Depth of recess m
i (index) Consecutive number 1
k Exponent 1
K Speed-dependent parameter 1
rot
K Normalized speed-dependent parameter 1
rot,nom
l Length in the direction of flow m
l Axial land length m
l Circumferential land length m
l Length of capillaries m
N Rotational frequency (speed) s
opt
optimum 1
(index)
p Recess pressure, general Pa
p Specific bearing load [ p = F/(B × D)]
p Feed pressure (pumping pressure) Pa
p Pressure in recess i Pa
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ISO/DIS 12167-1:2022(E)
Table 1 (continued)
Symbol Term Unit
P * Pressure ratio 1
p Pressure in recess i, when ε = 0 Pa
i, 0
P* Power ratio 1
P Frictional power W
p Maximum pressure in recess Pa
max
p Minimum pressure in recess Pa
min
P Frictional power in land area W
f,lan
P Frictional power in recess area W
f,p
Characteristic value for the frictional power 1
Characteristic value for the frictional power in land area 1
fl, an
P Characteristic value for the frictional power in recess area 1
fp,
P Pumping power W
P Total power W
tot
Characteristic value of total power 1
tot
Q Lubricant flow rate (for complete bearing) m /s
Q* Lubricant flow rate parameter 1
Q Lubricant flow rate from recess in the axial direction m /s
Q Lubricant flow rate from capillary into recess i m /s
cp, i
Q Inlet lubricant flow rate into recess in the circumferential direction m /s
Q Outlet lubricant flow rate from recess in the circumferential direction m /s
R Flow resistance of capillaries Pa⋅s/m
 
12××η l
R Flow resistance of one axial land R =  Pa⋅s/m
lan, ax lan,ax
 3 
bC×
 
ax R
 
12××η l
R Flow resistance of one circumferential land R = Pa⋅s/m
 
lan, c lan,c
 3 
bC×
 cR 
R Flow resistance of one recess, when ε = 0 Pa⋅s/m
P, 0
Re Reynolds number 1
Re Reynolds number in capillaries 1
Re Reynolds number in recess 1
So Sommerfeld number 1
T Temperature °C
T Mean temperature in the bearings; see Formula (15) °C
T Temperature in capillaries °C
T Inlet temperature °C
u Flow velocity m/s
U Circumferential speed m/s
w Average velocity in restrictor m/s
Z Number of recesses 1
Position of first recess related to recess centre measured from load direction;
α rad
see Figure A.3
β Attitude angle of shaft °
γ Exponent in viscosity formula 1
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ISO/DIS 12167-1:2022(E)
Table 1 (continued)
Symbol Term Unit
Δp Pressure difference in land area Pa
lan
ΔT Temperature difference K
ΔT Mean temperature difference in the bearings K
ΔT Temperature difference in capillaries K
ε Relative eccentricity 1
η Dynamic viscosity Pa⋅s
η Dynamic viscosity for TT= Pa⋅s
B B
η Dynamic viscosity in capillaries Pa⋅s
η Dynamic viscosity at 40 °C Pa⋅s
κ Resistance ratio 1
ξ Restrictor ratio 1
π Relative frictional pressure 1
π Optimum relative frictional pressure 1
f,opt
ρ Density kg/m
τ Shearing stress N/m
Angular coordinate measured from radius opposite to eccentricity, e;
φ rad
see Figure A.3
φ Angle of resultant force of recesses rad
φ Angle between the center of land and the center of drainage groove rad
ψ Relative bearing clearance 1
ψ Optimum relative bearing clearance 1
opt
ω Angular velocity (ω = 2 × π × Ν) s
5 Bases of calculation and boundary conditions

Calculation in accordance with this document is the mathematical determination of the operational

parameters of hydrostatic plain journal bearings as a function of operating conditions, bearing

geometry and lubrication data. This means the determination of eccentricities, load-carrying capacity,

stiffness, required feed pressure, oil flow rate, frictional and pumping power, and temperature rise.

Besides the hydrostatic pressure build up, the influence of hydrodynamic effects is also approximated.

Reynolds equation furnishes the theoretical basis for the calculation of hydrostatic bearings. In

most practical cases of application, it is, however, possible to arrive at sufficiently exact results by

approximation.

The approximation used in this document is based on two basic formulae intended to describe the

flow through the bearing lands, which can be derived from Reynolds equation when special boundary

conditions are observed. The Hagen-Poiseuille law describes the pressure flow in a parallel clearance

gap and the Couette formula the drag flow in the bearing clearance gap caused by shaft rotation. A

detailed presentation of the theoretical background of the calculation procedure is included in Annex A.

The following important premises are applicable to the calculation procedures described in this

document:
a) all lubricant flows in the lubrication clearance gap are laminar;
b) the lubricant adheres completely to the sliding surfaces;
c) the lubricant is an incompressible Newtonian fluid;
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ISO/DIS 12167-1:2022(E)

d) in the whole lubrication clearance gap, as well as in the preceding restrictors, the lubricant is

partially isoviscous;

e) a lubrication clearance gap completely filled with lubricant is the basis of frictional behaviour;

f) fluctuations of pressure in the lubricant film normal to the sliding surfaces do not take place;

g) bearing and journal have completely rigid surfaces;

h) the radii of curvature of the surfaces in relative motion to each other are large in comparison to the

lubricant film thickness;

i) the clearance gap height in the axial direction is constant (axial parallel clearance gap);

j) the pressure over the recess area is constant;
k) there is no motion normal to the sliding surfaces.

The bearing consists of Z cylindrical segments and rectangular recess of the same size and is

supplied with oil through restrictors of the same flow characteristics. Each segment consists of a

circumferential part between two centre lines of axial drainage grooves. With the aid of the above-

mentioned approximation formulae, all parameters required for the design or calculation of bearings

can be determined. The application of the similarity principle results in dimensionless similarity values

for load-carrying capacity, stiffness, oil flow rate, friction, recess pressures, etc.

The results indicated in this document in the form of tables and diagrams are restricted to operating

ranges common in practice for hydrostatic bearings. Thus, the range of the bearing eccentricity

(displacement under load) is limited to ε = 0 to 0,5.

Limitation to this eccentricity range means a considerable simplification of the calculation procedure

as the load-carrying capacity is a nearly linear function of the eccentricity. However, the applicability

of this procedure is hardly restricted as in practice eccentricities ε > 0,5 are mostly undesirable for

reasons of operational safety. A further assumption for the calculations is the approximated optimum

[1]
restrictor ratio ξ = 1 for the stiffness behaviour.

As for the outside dimensions of the bearing, this document is restricted to the range bearing width/

bearing diameter B/D = 0,3 to 1, which is common in practical cases of application. The recess depth is

larger than the clearance gap height by a factor of 10 to 100. When calculating the friction losses, the

friction loss over the recess in relation to the friction over the bearing lands can generally be neglected

on account of the above premises. However, this does not apply when the bearing shall be optimized

with regard to its total power losses.

To take into account the load direction of a bearing, it is necessary to distinguish between the two

extreme cases, load in the direction of recess centre and load in the direction of land centre.

Apart from the aforementioned boundary conditions, some other requirements are to be mentioned for

the design of hydrostatic bearings in order to ensure their functioning under all operating conditions.

In general, a bearing shall be designed in such a manner that a clearance gap height of at least 50 % to

60 % of the initial clearance gap height is ensured when the maximum possible load is applied. With

this in mind, particular attention shall be paid to misalignments of the shaft in the bearing due to

shaft deflection which may result in contact between shaft and bearing edge and thus in damage of the

bearing. In addition, the parallel clearance gap required for the calculation is no longer present in such

a case.

In the case where the shaft is in contact with the bearing lands when the hydrostatic pressure is

switched off, it might be necessary to check the contact zones with regard to rising surface pressures.

It shall be ensured that the heat originating in the bearing does not lead to a non-permissible rise in the

temperature of the oil.

If necessary, a means of cooling the oil shall be provided. Furthermore, the oil shall be filtered in order

to avoid choking of the capillaries and damage to the sliding surfaces.
© ISO 2022 – All rights reserved
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ISO/DIS 12167-1:2022(E)

Low pressure in the relieved recess shall also be avoided, as this leads to air being drawn in from the

environment and this would lead to a decrease in stiffness (see 6.7).
6 Method of calculation
6.1 General

This document covers the calculation, as well as the design, of hydrostatic plain journal bearings. In

this case, calculation is understood to be the verification of the operational parameters of a hydrostatic

bearing with known geometrical and lubrication data. In the case of a design calculation, with the given

methods of calculation, it is possible to determine the missing data for the required bearing geometry,

the lubrication data and the operational parameters on the basis of a few initial data (e.g. required load-

carrying capacity, stiffness, rotational frequency).

In both cases, the calculations are carried out according to an approximation method based on the

Hagen-Poiseuille and the Couette formulae, mentioned in Clause 5, see also A.2.2 and A.2.3. The bearing

parameters calculated according to this method are given as relative values in the form of tables and

diagrams as a function of different parameters. The procedure for the calculation or design of bearings

is described in 6.2 to 6.7. This includes the determination of different bearing parameters with the

aid of the given calculation formulae or the tables and diagrams. The following calculation items are

explained in detail:

a) determination of load-carrying capacity with and without taking into account shaft rotation;

b) calculation of lubricant flow rate and pumping power;

c) determination of frictional power with and without consideration of losses in the bearing recesses;

d) procedure for bearing optimization with regard to minimum total power loss.

For all calculations, it is necessary to check whether the important premise of laminar flow in the

bearing clearance gap, in the bearing recess and in the capillary is met. This is checked by determining

the Reynolds numbers. Furthermore, the portion of the inertia factor in the pressure differences shall

be kept low at the capillary (see A.3.1).

If the boundary conditions defined in Clause 5 are observed, this method of calculation yields results

with deviations which can be neglected for the requirements of practice, in comparison with an exact

calculation by solving the Reynolds equation.
6.2 Load-carrying capacity

Unless indicated otherwise, it is assumed in the following that capillaries with a linear characteristic

are used as restrictors and that the restrictor ratio is ξ = 1. Furthermore, the difference is only made

between the two cases, “load in direction of recess centre” and “load in direction of land centre”. For this

reason, it is no longer mentioned in each individual case that the characteristic values are a function of

the three parameters, “restrictor type”, “restrictor ratio” and “load direction relative to the bearing”.

Even under the abovementioned premises, the characteristic value of load carrying capacity

[Formula (1)]
F p
F = = (1)
BD××pp
en en
still depends on the following parameters:
— number of recesses, Z;
— width/diameter ratio, B/D;
— relative axial land width, l /B;
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ISO/DIS 12167-1:2022(E)
— relative land width in circumferential direction, l /D;
— relative groove width, b /D;
— relative journal eccentricity, ε;

— relative frictional pressure when the difference is only made between the two cases, “load on recess

centre” and “load on land centre”:
ηω×
π = (2)
p ×ψ

NOTE The Sommerfeld number, So, common with hydrodynamic plain journal bearings can be set up as

follows:
2 *
p×ψ F
So= =
ηω× π

In ISO 12167-2:2021, Figures 1 and 2, the functions F*(ε, π ) and β(ε, π ) are represented for Z = 4, ξ = 1,

f f

B/D = 1, l /B = 0,1, l /D = 0,1, b /D = 0,05, i.e. restriction by means of capillaries, load in direction of

ax c G
centre of bearing recess.

These figures show the influence of rotation on the characteristic value of load-carrying capacity and

the attitude angle.

For the calculation of a geometrically similar bearing, it is possible to determine the minimum lubricant

film thickness when values are given, e.g. for F, B, D, p , ω, ψ, and η (determination of η according to

en B B
6.6, if applicable).

All parameters are given for the determination of F* according to Formula (1) and π according to

Formula (2). For this geometry, the relevant values for ε and β can be taken from ISO 12167-2:2021,

Figures 1 and 2 and thus, h = C (1 − ε).
min R

According to the approximation method described in Annex A, it transpires that the characteristic

value of effective load-carrying capacity is no longer a function of the ratio B/D.

F F
F = = (3)
eff
b Zb×
bZ××bP×
cax
caxen
D B
If the resistance ratio
lb×
lan,ax
ax c
κ == (4)
R lb×
lan,c cax
and the speed dependent parameter
ξκ××π ×l
K =
rot
rot
K = (5)
rot,nom
1+κ
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ISO/DIS 12167-1:2022(E)
are introduced, there remains a dependence on the following parameters:
FZ(),,ϕκ,,K ε
effG rot

If, in addition, advantage is taken of the fact that the function F ()ε is nearly linear for ε ≤ 0,5, then it

eff

is practically sufficient to know that the function Ffεϕ=04,,= ZK,,κ for the calculation of

() ()
effG rot
the load carrying capacity.

For K = 0, i.e. for the stationary shaft, the characteristic value of effective load-carrying capacity for

rot
ε = 0,4 only depends on three parameters:
Ff()εϕ=04,,= ()Z ,κ
effG

Thus, in ISO 12167-2:2021, Figure 3, F ε =04, for Z = 4 and 6 can be given via κ for different φ

eff,0
values.

The influence of the rotational movement on the characteristic value of load-carrying capacity is taken

eff
into account by the ratio = fZ(),,ϕκ,K .
Grot
eff,0

For Z = 4, the ratio FF/ is shown in ISO 12167-2:2021, Figure 4. The hydrodynamically conditioned

effeff,0

increase of the load-carrying capacity can be easily recognized when presented in such a manner.

If, e.g. Z and all parameters are given for the determination of F according to Formula

...